This paper deals with the problem of clustering a data-set. In
particular, the bisecting divisive approach is here considered. This approach
can be naturally divided into two sub-problems: the problem of choosing which
cluster must be divided, and the problem of splitting the selected cluster. The
focus here is on the first problem. The contribution of this work is to propose
a new technique for the selection of the cluster to split. This technique is
based upon the shape of the cluster. This result is presented with reference to
two specific splitting algorithms: the celebrated bisecting K-means algorithm,
and the recently proposed Principal Direction Divisive Partitioning (PDDP)
algorithm. The problem of evaluating the quality of a partition is also
discussed.